Roles of $\Delta(1232)$, $N^*(1520)$, and $N^*(1650)$ resonances in $\gamma p\to \pi^0 \pi^0 p$ reaction within an effective Lagrangian approach

TL;DR

This study investigates the roles of specific baryon resonances in the gamma-proton to two neutral pions and a proton reaction near threshold using an effective Lagrangian approach, successfully reproducing experimental data.

Contribution

It introduces a detailed analysis of resonance contributions in the reaction, highlighting the mechanisms of production and providing a framework for future experimental exploration.

Findings

Delta(1232) mainly from s-channel nucleon pole

N*(1520) and N*(1650) from t-channel rho exchange

Reproduces experimental differential cross sections accurately

Abstract

Roles of the $\Delta (1232)$, ${N}^{*}(1520)$, and ${N}^{*}(1650)$ resonances in the $\gamma p\to{\pi }^{0}{\pi }^{0}p $ reaction near threshold is investigated within an effective Lagrangian approach. We have calculated the differential cross sections of the $\gamma p\to{\pi }^{0}{\pi }^{0}p$ reaction by including the contributions from the $\Delta (1232)$, ${N}^{*}(1520)$, and ${N}^{*}(1650)$ intermediate states decaying into $\pi^0 p$ via the $s$-channel nucleon pole and $t$-channel $\rho$ exchange, and found that the current experimental measurements can be well reproduced. The production of $\Delta(1232)$ is mainly from the mechanism of the $s$-channel nucleon pole, while the ${N}^{*}(1520)$ and ${N}^{*}(1650)$ are produced from the mechanism of the $t$-channel $\rho$ exchange. It is expected that more experimental data on the $\gamma p \to \pi^0 \pi^0 p$ reaction can be used to explore the properties of the low-lying excited baryon states and also the scalar $f_0(500)$ and $f_0(980)$ mesons.